9231 P42 - Nov 2023 - Q2 - 8 marks
6698
The number of breakdowns on a particular section of road is recorded each day over a period of 90 days. It is suggested that the number of breakdowns follows a Poisson distribution with mean 3.5. The data is summarised in the table, together with some of the expected frequencies resulting from the suggested Poisson distribution.
| Number of breakdowns per day | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 or more |
|---|---|---|---|---|---|---|---|---|---|
| Observed frequency | 0 | 5 | 13 | 17 | 21 | 16 | 9 | 5 | 4 |
| Expected frequency | 2.718 | 9.512 | 16.646 | 16.993 | 11.895 | 3.469 | 2.407 |
(a) Complete the table.
(b) Carry out a goodness of fit test, at the \(10\%\) significance level, to determine whether or not \(\operatorname{Po}(3.5)\) is a good fit to the data.
Solutions and mark schemes for 9231 are temporarily available to admins only.